Abstract
The multiple fatigue cracks in various location of the same structural element usually appear simultaneously. The multiple fatigue cracks may link up to form a large crack, which will lead to the residual strength of structure decrease sharply. The structure failure depends on the crack linkup and propagation under cyclic loading. In order to solve the multiple fatigue crack problem, this study simulates the longest crack growth behavior by using piecewise deterministic Markov processes (PDMP) and evaluate the dynamic reliability by Monte Carlo method. The Forman model is used to calculate the crack growth rate, which considered the stress ratio and critical stress intensity factor effects. The whole trajectory of the longest crack growth is divided into several states based on the crack merging, which has explicit physical meaning. The uncertainties of material properties in each state are quantified. The fatigue crack state transition probability matrix, initial law and state space are determined. Based on the established PDMP, the dynamic reliability is evaluated by using the Monte Carlo method. The sample data from literature is used to calibrate the parameters associated to PDMP. The simulated crack growth behavior and reliability value can match the sample data well. It manifests that the proposed approach can evaluate the dynamic reliability of multiple-crack system precisely and effectively.
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